Your home county is just completely wrong in their understanding.
Top 3 Ancestry groups (2015 Census) are actually 1) German, 2) Black/African-American and 3) Mexican. English comes in #5. [1]
If you tally English/Scottish/Welsh, you are only talking about 10% of the US population is British descent. And that was from the Census in 2015. In 2020 they had a White category which was #1, and only 8.2M identified explicitly as English and 1.75M as Welsh.
> if you relocated the population of say Bangladesh to the US, and gave everyone US citizenship, they wouldn’t suddenly become “American.”
They would. You don't have to adhere to some sort of defined American culture or fully assimilate into it, it's not Denmark. If you travel to NYC, Miami, Atlanta, New Orleans, Iowa, LA, San Fran, Dallas, Seattle, you are going to get different people and experiences and cultures. I can assure you they are all very much Americans.
I'd argue that those that worry about a scale of Americanism and where they'd place their own fellow citizens are actually the least American if anything. We can call it the American Culture Paradox. Those that think they are the most American and categorize or judge others are actually the least American!
> The American founders clearly recognized as much when they created a distinction between native-born citizens and naturalized citizens and wrote it into the Constitution.
Yes because they had such massive distrust for the monarchy they didn't want outsiders infiltrating and taking over their new government and country.
[1] https://www.infoplease.com/us/race/ancestry-us-population-ra... (2015 Results)